Knotted families from graspers

2023/07/26 by Kosanović, Danica
#55Q15 (Secondary) #57K45 (Primary) 57K12 #57R40 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2307.14028

Abstract

For any smooth manifold M of dimension d≥4 we construct explicit classes in homotopy groups of spaces of embeddings of either an arc or a circle into M, in every degree that is a multiple of d-3, and show that they are detected in the Taylor tower of Goodwillie and Weiss. The classes are obtained from families of string links constructed in the d-ball.

Related

• Diffeomorphisms of 4-manifolds from graspers
• On homotopy groups of spaces of embeddings of an arc or a circle: the Dax invariant
• Invariants of knotted surfaces from link homology and bridge trisections
• From disc patterns in the plane to character varieties of knot groups
• Spaces of knots in the solid torus, knots in the thickened torus, and\n links in the 3-sphere